Skip to main content
SpringerLink
Log in

The classification problem for simple lie algebras of characteristic p

  • Conference paper
  • First Online:
Lie Algebras and Related Topics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 933))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • [Bn] Benkart, G. M.: On inner ideals and ad-nilpotent elements of Lie algebras. Trans. Amer. Math. Soc. 232 (1977), 61–81.

    Article  MathSciNet  MATH  Google Scholar 

  • [B-I] Benkart, G. M., Isaacs, I. M.: Lie algebras with nilpotent centralizers. Canad. J. Math. 31 (1979), 929–941.

    Article  MathSciNet  MATH  Google Scholar 

  • [B-I-O] Benkart, G. M., Isaacs, I. M., Osborn, J. M.: Lie algebras with self-centralizing ad-nilpotent elements. J. Algebra 57 (1979), 279–309.

    Article  MathSciNet  MATH  Google Scholar 

  • [Bl 1] Block, R. E.: Trace forms on Lie algebras. Can. J. Math. 14 (1962), 553–564.

    Article  MathSciNet  MATH  Google Scholar 

  • [Bl 2] Block, R. E.: On the Mills-Seligman axioms for Lie algebras of classical type. Trans. Amer. Math. Soc. 121 (1966), 378–392.

    Article  MathSciNet  MATH  Google Scholar 

  • [Bl 3] Block, R. E.: Determination of the differentiably simple rings with a minimal ideal. Ann. of Math. (2) 90 (1969), 433–459.

    Article  MathSciNet  MATH  Google Scholar 

  • [Bl 4] Block, R. E.: Irreducible representations of Lie algebra extensions. Bull. Amer. Math. Soc. 8 (1974), 868–872.

    Article  MathSciNet  MATH  Google Scholar 

  • [Bl 5] Block, R. E.: Restricted simple Lie algebras of rank 2 or of toral rank 2. 1981 Yale Conference Proceedings, Contemporary Math., Amer. Math. Soc. (In press).

    Google Scholar 

  • [B-W 1] Block, R. E., Wilson, R. L.: On filtered Lie algebras and divided power algebras. Comm. in Algebra 3 (1975), 571–589.

    Article  MathSciNet  MATH  Google Scholar 

  • [B-W 2] Block, R. E., Wilson, R. L.: The simple Lie p-algebras of rank two. Ann of Math. (In press).

    Google Scholar 

  • [Dm 1] Demuskin, S. P.: Cartan subalgebras of the simple Lie p-algebras Wn and Sn (Russian). Sibirsk. Mat. Z. 11 (1970) 310–325; English transl., Siberian Math. J. 11 (1970) 233–245.

    MathSciNet  MATH  Google Scholar 

  • [Dm 2] Demuskin, S. P.: Cartan subalgebras of simple nonclassical Lie p-algebras (Russian). Izv. Akad. Nauk SSSR Ser. Math. 36 (1972), 915–932; English transl., Math. USSR-Izv. 6 (1972), 905–924.

    MathSciNet  Google Scholar 

  • [El] El’sting, G. O.: Izv. Vysš. Učebn. Zaved. Matematika 4 (1981), 64–68.

    MathSciNet  Google Scholar 

  • [Er] Ermolaev, Yu. B.: Izv. Vysš. Učebn. Zaved. Matematika 7 (1981), 80–84, 8 (1981) 66–70, 8 (1981), 70–74.

    MathSciNet  Google Scholar 

  • [Gr 1] Gregory, T. B.: Simple Lie algebras with classical reductive null component. J. Algebra 63 (1980), 484–493.

    Article  MathSciNet  MATH  Google Scholar 

  • [Gr 2] Gregory, T. B.: A characterization of the contact Lie algebras. Proc. Amer. Math. Soc. 82 (1981), 505–511.

    Article  MathSciNet  MATH  Google Scholar 

  • [Gr 3] Gregory, T. B.: On simple reducible Lie algebras of depth two. Proc. Amer. Math. Soc. 83 (1981), 31–35.

    Article  MathSciNet  MATH  Google Scholar 

  • [Jc] Jacobs, J. B.: On classifying simple Lie algebras of prime characteristic by nilpotent elements. J. Algebra 19 (1971), 31–50.

    Article  MathSciNet  MATH  Google Scholar 

  • [Kc 1] Kac, V. G.: The classification of the simple Lie algebras over a field with non-zero characteristic (Russian). Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970), 385–408; English transl., Math. USSR-Izv. 4 (1970), 391–413.

    MathSciNet  Google Scholar 

  • [Kc 2] Kac, V. G.: Description of filtered Lie algebras with which grade Lie algebras of Cartan type are associated (Russian). Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), 800–838; Errata 40 (1976), 1415; English transl. Math. USSR-Iva, 8 (1974), 801–835; Errata, 10 (1976), 1339.

    MathSciNet  Google Scholar 

  • [Kp 1] Kaplansky, I.: Lie algebras of characreristic p. Trans. Amer. Math. Soc. 89 (1958), 149–183.

    MathSciNet  MATH  Google Scholar 

  • [Kp 2] Kaplansky, I.: Lie algebras and locally compact groups. University of Chicago Press (1971).

    Google Scholar 

  • [Ks 1] Kostrikin, A. I.: Simple Lie p-algebras (Russian). Trudy Mat. Inst. Steklov 64 (1961), 78–89; English transl., Amer. Math. Soc. Transl. Ser. (2) 55 (1966), 195–206.

    MathSciNet  MATH  Google Scholar 

  • [Ks 2] Kostrikin, A. I.: Squares of adjoint endomorphisms in simple Lie p-algebras (Russian). Izv. Akad. Nauk SSSR Ser. Mat. 31 (1967), 445–487; English transl., Math. USSR-Izv. 1 (1967), 434–473.

    MathSciNet  MATH  Google Scholar 

  • [Ks 3] Kostrikin, A. I.: Variations modulaires sur un theme de Cartan. Actes. Congres Intern. Math. Tome 1 (1970) 285–292.

    MathSciNet  Google Scholar 

  • [K-S 1] Kostrikin, A. I., Šafarevič, I. R.: Cartan pseudogroups and Lie p-algebras (Russian). Dokl. Akad. Naud SSSR 168 (1966), 740–742; English transl., Soviet Math. Dokl. 7 (1966), 715–718.

    Google Scholar 

  • [K-S 2] Kostrikin, A. I., Šafarevič, I. R.: Graded Lie algebras of finite characteristic (Russian). Izv. Akad. Nauk SSSR Ser. Mat. 33 (1969), 251–322; English transl., Math. USSR-Irv. 3 (1969), 237–304.

    MathSciNet  Google Scholar 

  • [Kr] Krylyuk, Ja. C.: Uspehi Mat. Nauk (1979), 203–204.

    Google Scholar 

  • [Kz 1] Kuznetsov, M. K.: Simple modular Lie algebras with a solvable maximal subalgebra (Russian). Mat. Sbornik 101 (1976), 77–86.

    MATH  Google Scholar 

  • [Kz 2] Kuznetsov, M. K.: Mat. Sb. (To appear).

    Google Scholar 

  • [Kz 3] Kuznetsov, M. K.: (To appear).

    Google Scholar 

  • [M-S] Mills, W. M., Seligman, G. B.: Lie algebras of classical type. J. Math. Mech. 6 (1957), 519–548.

    MathSciNet  MATH  Google Scholar 

  • [Sc] Schue, J. R.: Cartan decompositions for Lie algebras of prime characteristic. J. Algebra 11 (1969), 25–52; Erratum 13 (1969), 558.

    Article  MathSciNet  MATH  Google Scholar 

  • [Sl 1] Seligman, G. B.: On Lie algebras of prime characteristic. Mem. Amer. Math. Soc. 19 (1956).

    Google Scholar 

  • [Sl 2] Seligman, G. B.: Modular Lie algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 40. Springer-Verlag New York, Inc., New York, (1967).

    Google Scholar 

  • [Sr] Serconek, S.: Finite Cartan matrices and Lie algebras of classical type. J. Algebra.

    Google Scholar 

  • [St] Strade, H.: Nonclassical simple Lie algebras and strong degeneration. Arch. Math. (Basel) 24 (1973), 482–485.

    Article  MathSciNet  MATH  Google Scholar 

  • [Ty] Tyurin, S. A.: Mat. Zametki (1978).

    Google Scholar 

  • [Ws 1] Weisfeiler, B. Ju.: On the structure of the minimal ideal of some graded Lie algebras in characteristic p>0. J. Algebra 53 (1978), 344–361.

    Article  MathSciNet  MATH  Google Scholar 

  • [Ws 2] Weisfeiler, B. Ju.: (To appear).

    Google Scholar 

  • [W-K] Weisfeiler, B. Ju., Kac, V. G.: Exponentials in Lie algebras of characteristic p (Russian). Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), 762–788; English transl., Math. USSR-Izv. 5 (1971), 777–803.

    MathSciNet  MATH  Google Scholar 

  • [Wl 1] Wilson, R. L.: Classification of generalized Witt algebras over algebraically closed fields. Trans. Amer. Math. Soc. 153 (1971), 191–210.

    Article  MathSciNet  MATH  Google Scholar 

  • [Wl 2] Wilson, R. L.: The roots of a simple Lie algebra are linear. Bull. Amer. Math. Soc. 82 (1976), 607–608.

    Article  MathSciNet  MATH  Google Scholar 

  • [Wl 3] Wilson, R. L.: A structural characterization of the simple Lie algebras of generalized Cartan type over fields of prime characteristic. J. Algebra 40 (1976), 418–465.

    Article  MathSciNet  MATH  Google Scholar 

  • [Wl 4] Wilson, R. L.: Simple Lie algebras of toral rank one. Trans. Amer. Math. Soc. 236 (1978), 287–295.

    Article  MathSciNet  MATH  Google Scholar 

  • [Wl 5] Wilson, R. L.: Simple Lie algebras of type S. J. Algebra 62 (1980), 292–298.

    Article  MathSciNet  MATH  Google Scholar 

  • [Wl 6] Wilson, R. L.: A “new” proof of Kaplansky’s theorem on simple Lie algebras of rank one. Algebra Carbondale 1980, Proceedings, Lect. Notes in Math. 848, Springer-Verlag (1981), 1–12.

    Article  Google Scholar 

  • [Wl 7] Wilson, R. L.: The classification problem for simple Lie algebras of characteristic p. Algebra Carbondale 1980, Proceedings, Lect. Notes in Math. 848, Springer-Verlag (1981), 13–32.

    Article  MathSciNet  Google Scholar 

  • [Wl 8] Wilson, R. L.: Restricted simple Lie algebras with toral Cartan subalgebras. 1981 Yale Conference Proceedings, Contemporary Math., Amer. Math. Soc. (In press).

    Google Scholar 

  • [Wn 1] Winter, D. J.: On the toral structure of Lie p-algebras. Acta Math. 123 (1969), 70–81.

    Article  MathSciNet  MATH  Google Scholar 

  • [Wn 2] Winter, D. J.: Triangulable subalgebras of Lie p-algebras. Pac. J. Math. 81 (1979), 273–281.

    Article  MathSciNet  MATH  Google Scholar 

  • [Wn 3] Winter, D. J.: Cartan decompositions and Engel subalgebra triangulability. J. Algebra 62 (1980), 400–417.

    Article  MathSciNet  MATH  Google Scholar 

  • [Wn 4] Winter, D. J.: A combinatorial theory of symmetry and applications to Lie algebras. Algebra Carbondale 1980, Proceedings, Lect. Notes in Math. 848, Springer-Verlag (1981), 41–62.

    Article  MathSciNet  Google Scholar 

  • [Wn 5] Winter, D. J.: Symmetrysets, J. Alg., 73 (1981), 238–247.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of California, Riverside, 92521, Riverside, CA

    Richard E. Block

Authors
  1. Richard E. Block
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

David Winter

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Block, R.E. (1982). The classification problem for simple lie algebras of characteristic p. In: Winter, D. (eds) Lie Algebras and Related Topics. Lecture Notes in Mathematics, vol 933. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093351

Download citation

  • DOI: https://doi.org/10.1007/BFb0093351

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11563-2

  • Online ISBN: 978-3-540-39262-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation